The magnetic field at the point of intersection of diagonals of a square wire loop of side L carrying a current I is

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{\mathrm{\pi L}}$

• $\frac{2{\mathrm{\mu }}_0\mathrm{I}}{\mathrm{\pi L}}$

• $\frac{\sqrt{2} {\mathrm{\mu }}_0\mathrm{I}}{\mathrm{\pi L}}$

• $\frac{2\sqrt{2} {\mathrm{\mu }}_0\mathrm{I}}{\mathrm{\pi L}}$

Four charges equal to -Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is

• $\frac{-\mathrm{Q}}{4}\left(1 + 2\sqrt{2}\right)$

• $\frac{\mathrm{Q}}{4}\left(1 + 2\sqrt{2}\right)$

• $\frac{-\mathrm{Q}}{2}\left(1 + 2\sqrt{2}\right)$

• $\frac{\mathrm{Q}}{2}\left(1 + 2\sqrt{2}\right)$

A radioactive nucleus of mass number A, initially at rest, emits an α-particle with a speed v. The recoil speed of the daughter nucleus will be

• $\frac{2\mathrm{v}}{\mathrm{A} - 4}$

• $\frac{2\mathrm{v}}{\mathrm{A} + 4}$

• $\frac{4\mathrm{v}}{\mathrm{A} - 4}$

• $\frac{4\mathrm{v}}{\mathrm{A} + 4}$

In the nuclear reaction ${}_7{}^{14}\mathrm{N} + \mathrm{X} \underset{}{\to } {}_6{}^{14}\mathrm{C} + {}_1{}^1\mathrm{H}$, the X will be

• ${}_{-1}{}^0\mathrm{e}$

• ${}_1{}^1\mathrm{H}$

• ${}_1{}^2\mathrm{H}$

• ${}_0{}^1\mathrm{n}$

35.

Which type of gate the following truth table represents ?

     

• NOT

• AND

• OR

• NAND

In Young's double slit experiment the two slits are d distance apart. Interference pattern is observed on a screen at a distance D from the slits. A dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is

• $\frac{{\mathrm{D}}^2}{2\mathrm{d}}$

• $\frac{{\mathrm{d}}^2}{2\mathrm{D}}$

• $\frac{{\mathrm{D}}^2}{\mathrm{d}}$

• $\frac{{\mathrm{d}}^2}{\mathrm{D}}$

Two thin lenses of focal lengths 20 cm and 25 cm are placed in contact. The effective power of the combination is

• 9 D

• 2 D

• 3 D

• 7 D

A convex lens of focal length 30 cm produces 5 times magnified real image of an object. What is the object distance?

• 36 cm

• 25 cm

• 30 cm

• 150 cm

If the focal length of the eye-piece of a telescope is doubled, its magnifying power (m) will be

• 2 m

• 3 m

• $\frac{\mathrm{m}}{2}$

• 4 m

A plano-concave lens is made of glass of refractive index 1.5 and the radius of curvature of its curved face is 100 cm. What is the power of the lens ?

• + 0.5 D

• − 0.5 D

• − 2 D

• + 2 D